Can the Regi Trio and Rayquaza be respawned in their locations if you kill or run from them in Emerald

There is actually a special emulator you can use to trade between games called VBALink (and is based off of Visual Boy Advanced). If you had another game, you could trade between copies and get all of the Pokemon.

An alternate is to use cheats to "encounter" them in the wild, which most all emulators provide built in.

What's happening here is that you are dying after you defeat the first member of the elite four, which halves your total money. Since you weren't checking your money between defeating the first member and losing to the second member, it appeared that you were getting half as much money as you really were, since you immediately lose half of all the money you get.